A concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered...

This paper presents a concise and efficient scattering matrix formalism for stable analysis of elastic wave propagation in multilayered anisotropic solids. The formalism is capable of resolving completely the numerical instability problems associated with transfer matrix method, thereby obviating the extensive reformulation in its modified versions based on delta operator technique. In contrast to the earlier reflection matrix formalisms, all scattering matrices are obtained in a direct manner without invoking wave-propagator or scatterer operator concepts. Both local and global reflection and transmission matrices corresponding to scatterings in two and more layers are derived. The derivation of global scattering matrices in terms of the local ones is carried out concisely based on physical arguments to provide better insights into scattering mechanism. Another formulation which is even more succinct is also devised for obtaining the global scattering matrices directly from eigensolutions. The resultant expressions and algorithm are terse, efficient and convenient for implementation.